LMFDB - Embedded newform 8018.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.03614 q^{3} +1.00000 q^{4} +0.118794 q^{5} -1.03614 q^{6} +2.13406 q^{7} +1.00000 q^{8} -1.92642 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.03614 q^{3} +1.00000 q^{4} +0.118794 q^{5} -1.03614 q^{6} +2.13406 q^{7} +1.00000 q^{8} -1.92642 q^{9} +0.118794 q^{10} +5.30344 q^{11} -1.03614 q^{12} +0.953466 q^{13} +2.13406 q^{14} -0.123087 q^{15} +1.00000 q^{16} -1.40790 q^{17} -1.92642 q^{18} -1.00000 q^{19} +0.118794 q^{20} -2.21118 q^{21} +5.30344 q^{22} -7.01405 q^{23} -1.03614 q^{24} -4.98589 q^{25} +0.953466 q^{26} +5.10445 q^{27} +2.13406 q^{28} -3.22709 q^{29} -0.123087 q^{30} +5.86651 q^{31} +1.00000 q^{32} -5.49510 q^{33} -1.40790 q^{34} +0.253514 q^{35} -1.92642 q^{36} +9.27789 q^{37} -1.00000 q^{38} -0.987923 q^{39} +0.118794 q^{40} +6.08967 q^{41} -2.21118 q^{42} +11.1940 q^{43} +5.30344 q^{44} -0.228847 q^{45} -7.01405 q^{46} +5.03802 q^{47} -1.03614 q^{48} -2.44578 q^{49} -4.98589 q^{50} +1.45878 q^{51} +0.953466 q^{52} -12.2837 q^{53} +5.10445 q^{54} +0.630018 q^{55} +2.13406 q^{56} +1.03614 q^{57} -3.22709 q^{58} -6.60513 q^{59} -0.123087 q^{60} +8.99482 q^{61} +5.86651 q^{62} -4.11109 q^{63} +1.00000 q^{64} +0.113266 q^{65} -5.49510 q^{66} +5.49250 q^{67} -1.40790 q^{68} +7.26753 q^{69} +0.253514 q^{70} +13.7678 q^{71} -1.92642 q^{72} +13.0402 q^{73} +9.27789 q^{74} +5.16607 q^{75} -1.00000 q^{76} +11.3179 q^{77} -0.987923 q^{78} +9.40559 q^{79} +0.118794 q^{80} +0.490332 q^{81} +6.08967 q^{82} -1.93571 q^{83} -2.21118 q^{84} -0.167250 q^{85} +11.1940 q^{86} +3.34371 q^{87} +5.30344 q^{88} -16.4497 q^{89} -0.228847 q^{90} +2.03476 q^{91} -7.01405 q^{92} -6.07852 q^{93} +5.03802 q^{94} -0.118794 q^{95} -1.03614 q^{96} -5.85181 q^{97} -2.44578 q^{98} -10.2166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.03614	−0.598215	−0.299107	−	0.954219i	$-0.596689\pi$
$3$	−1.03614	−0.598215	−0.299107	+	0.954219i	$0.596689\pi$
$4$	1.00000	0.500000
$5$	0.118794	0.0531263	0.0265632	−	0.999647i	$-0.491544\pi$
$5$	0.118794	0.0531263	0.0265632	+	0.999647i	$0.491544\pi$
$6$	−1.03614	−0.423002
$7$	2.13406	0.806600	0.403300	−	0.915068i	$-0.367863\pi$
$7$	2.13406	0.806600	0.403300	+	0.915068i	$0.367863\pi$
$8$	1.00000	0.353553
$9$	−1.92642	−0.642139
$10$	0.118794	0.0375660
$11$	5.30344	1.59905	0.799524	−	0.600634i	$-0.205085\pi$
$11$	5.30344	1.59905	0.799524	+	0.600634i	$0.205085\pi$
$12$	−1.03614	−0.299107
$13$	0.953466	0.264444	0.132222	−	0.991220i	$-0.457789\pi$
$13$	0.953466	0.264444	0.132222	+	0.991220i	$0.457789\pi$
$14$	2.13406	0.570352
$15$	−0.123087	−0.0317810
$16$	1.00000	0.250000
$17$	−1.40790	−0.341466	−0.170733	−	0.985317i	$-0.554614\pi$
$17$	−1.40790	−0.341466	−0.170733	+	0.985317i	$0.554614\pi$
$18$	−1.92642	−0.454061
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.118794	0.0265632
$21$	−2.21118	−0.482520
$22$	5.30344	1.13070
$23$	−7.01405	−1.46253	−0.731265	−	0.682093i	$-0.761070\pi$
$23$	−7.01405	−1.46253	−0.731265	+	0.682093i	$0.761070\pi$
$24$	−1.03614	−0.211501
$25$	−4.98589	−0.997178
$26$	0.953466	0.186990
$27$	5.10445	0.982352
$28$	2.13406	0.403300
$29$	−3.22709	−0.599255	−0.299628	−	0.954056i	$-0.596862\pi$
$29$	−3.22709	−0.599255	−0.299628	+	0.954056i	$0.596862\pi$
$30$	−0.123087	−0.0224725
$31$	5.86651	1.05366	0.526829	−	0.849972i	$-0.323381\pi$
$31$	5.86651	1.05366	0.526829	+	0.849972i	$0.323381\pi$
$32$	1.00000	0.176777
$33$	−5.49510	−0.956575
$34$	−1.40790	−0.241453
$35$	0.253514	0.0428517
$36$	−1.92642	−0.321069
$37$	9.27789	1.52528	0.762638	−	0.646825i	$-0.223904\pi$
$37$	9.27789	1.52528	0.762638	+	0.646825i	$0.223904\pi$
$38$	−1.00000	−0.162221
$39$	−0.987923	−0.158194
$40$	0.118794	0.0187830
$41$	6.08967	0.951046	0.475523	−	0.879703i	$-0.342259\pi$
$41$	6.08967	0.951046	0.475523	+	0.879703i	$0.342259\pi$
$42$	−2.21118	−0.341193
$43$	11.1940	1.70707	0.853537	−	0.521032i	$-0.174453\pi$
$43$	11.1940	1.70707	0.853537	+	0.521032i	$0.174453\pi$
$44$	5.30344	0.799524
$45$	−0.228847	−0.0341145
$46$	−7.01405	−1.03417
$47$	5.03802	0.734871	0.367435	−	0.930049i	$-0.380236\pi$
$47$	5.03802	0.734871	0.367435	+	0.930049i	$0.380236\pi$
$48$	−1.03614	−0.149554
$49$	−2.44578	−0.349397
$50$	−4.98589	−0.705111
$51$	1.45878	0.204270
$52$	0.953466	0.132222
$53$	−12.2837	−1.68729	−0.843647	−	0.536898i	$-0.819596\pi$
$53$	−12.2837	−1.68729	−0.843647	+	0.536898i	$0.819596\pi$
$54$	5.10445	0.694628
$55$	0.630018	0.0849516
$56$	2.13406	0.285176
$57$	1.03614	0.137240
$58$	−3.22709	−0.423737
$59$	−6.60513	−0.859914	−0.429957	−	0.902849i	$-0.641471\pi$
$59$	−6.60513	−0.859914	−0.429957	+	0.902849i	$0.641471\pi$
$60$	−0.123087	−0.0158905
$61$	8.99482	1.15167	0.575834	−	0.817566i	$-0.304677\pi$
$61$	8.99482	1.15167	0.575834	+	0.817566i	$0.304677\pi$
$62$	5.86651	0.745048
$63$	−4.11109	−0.517949
$64$	1.00000	0.125000
$65$	0.113266	0.0140489
$66$	−5.49510	−0.676400
$67$	5.49250	0.671015	0.335508	−	0.942037i	$-0.391092\pi$
$67$	5.49250	0.671015	0.335508	+	0.942037i	$0.391092\pi$
$68$	−1.40790	−0.170733
$69$	7.26753	0.874908
$70$	0.253514	0.0303007
$71$	13.7678	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$71$	13.7678	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$72$	−1.92642	−0.227030
$73$	13.0402	1.52624	0.763119	−	0.646258i	$-0.223667\pi$
$73$	13.0402	1.52624	0.763119	+	0.646258i	$0.223667\pi$
$74$	9.27789	1.07853
$75$	5.16607	0.596526
$76$	−1.00000	−0.114708
$77$	11.3179	1.28979
$78$	−0.987923	−0.111860
$79$	9.40559	1.05821	0.529106	−	0.848556i	$-0.322527\pi$
$79$	9.40559	1.05821	0.529106	+	0.848556i	$0.322527\pi$
$80$	0.118794	0.0132816
$81$	0.490332	0.0544814
$82$	6.08967	0.672491
$83$	−1.93571	−0.212472	−0.106236	−	0.994341i	$-0.533880\pi$
$83$	−1.93571	−0.212472	−0.106236	+	0.994341i	$0.533880\pi$
$84$	−2.21118	−0.241260
$85$	−0.167250	−0.0181408
$86$	11.1940	1.20708
$87$	3.34371	0.358483
$88$	5.30344	0.565349
$89$	−16.4497	−1.74367	−0.871833	−	0.489802i	$-0.837069\pi$
$89$	−16.4497	−1.74367	−0.871833	+	0.489802i	$0.837069\pi$
$90$	−0.228847	−0.0241226
$91$	2.03476	0.213300
$92$	−7.01405	−0.731265
$93$	−6.07852	−0.630313
$94$	5.03802	0.519632
$95$	−0.118794	−0.0121880
$96$	−1.03614	−0.105750
$97$	−5.85181	−0.594161	−0.297080	−	0.954852i	$-0.596013\pi$
$97$	−5.85181	−0.594161	−0.297080	+	0.954852i	$0.596013\pi$
$98$	−2.44578	−0.247061
$99$	−10.2166	−1.02681
$100$	−4.98589	−0.498589
$101$	−9.55441	−0.950699	−0.475350	−	0.879797i	$-0.657678\pi$
$101$	−9.55441	−0.950699	−0.475350	+	0.879797i	$0.657678\pi$
$102$	1.45878	0.144441
$103$	2.27475	0.224137	0.112069	−	0.993700i	$-0.464252\pi$
$103$	2.27475	0.224137	0.112069	+	0.993700i	$0.464252\pi$
$104$	0.953466	0.0934950
$105$	−0.262676	−0.0256345
$106$	−12.2837	−1.19310
$107$	−6.34312	−0.613212	−0.306606	−	0.951837i	$-0.599193\pi$
$107$	−6.34312	−0.613212	−0.306606	+	0.951837i	$0.599193\pi$
$108$	5.10445	0.491176
$109$	−1.82964	−0.175248	−0.0876240	−	0.996154i	$-0.527927\pi$
$109$	−1.82964	−0.175248	−0.0876240	+	0.996154i	$0.527927\pi$
$110$	0.630018	0.0600698
$111$	−9.61318	−0.912443
$112$	2.13406	0.201650
$113$	−1.20232	−0.113105	−0.0565526	−	0.998400i	$-0.518011\pi$
$113$	−1.20232	−0.113105	−0.0565526	+	0.998400i	$0.518011\pi$
$114$	1.03614	0.0970433
$115$	−0.833228	−0.0776989
$116$	−3.22709	−0.299628
$117$	−1.83677	−0.169810
$118$	−6.60513	−0.608051
$119$	−3.00455	−0.275426
$120$	−0.123087	−0.0112363
$121$	17.1265	1.55696
$122$	8.99482	0.814353
$123$	−6.30974	−0.568930
$124$	5.86651	0.526829
$125$	−1.18626	−0.106103
$126$	−4.11109	−0.366245
$127$	−0.441724	−0.0391966	−0.0195983	−	0.999808i	$-0.506239\pi$
$127$	−0.441724	−0.0391966	−0.0195983	+	0.999808i	$0.506239\pi$
$128$	1.00000	0.0883883
$129$	−11.5986	−1.02120
$130$	0.113266	0.00993410
$131$	−2.39368	−0.209137	−0.104568	−	0.994518i	$-0.533346\pi$
$131$	−2.39368	−0.209137	−0.104568	+	0.994518i	$0.533346\pi$
$132$	−5.49510	−0.478287
$133$	−2.13406	−0.185047
$134$	5.49250	0.474480
$135$	0.606379	0.0521888
$136$	−1.40790	−0.120726
$137$	19.6296	1.67707	0.838536	−	0.544847i	$-0.183412\pi$
$137$	19.6296	1.67707	0.838536	+	0.544847i	$0.183412\pi$
$138$	7.26753	0.618653
$139$	2.21189	0.187610	0.0938048	−	0.995591i	$-0.470097\pi$
$139$	2.21189	0.187610	0.0938048	+	0.995591i	$0.470097\pi$
$140$	0.253514	0.0214258
$141$	−5.22009	−0.439611
$142$	13.7678	1.15537
$143$	5.05665	0.422859
$144$	−1.92642	−0.160535
$145$	−0.383359	−0.0318362
$146$	13.0402	1.07921
$147$	2.53417	0.209014
$148$	9.27789	0.762638
$149$	−2.85546	−0.233928	−0.116964	−	0.993136i	$-0.537316\pi$
$149$	−2.85546	−0.233928	−0.116964	+	0.993136i	$0.537316\pi$
$150$	5.16607	0.421808
$151$	2.63738	0.214627	0.107313	−	0.994225i	$-0.465775\pi$
$151$	2.63738	0.214627	0.107313	+	0.994225i	$0.465775\pi$
$152$	−1.00000	−0.0811107
$153$	2.71220	0.219269
$154$	11.3179	0.912021
$155$	0.696907	0.0559769
$156$	−0.987923	−0.0790971
$157$	−12.5380	−1.00064	−0.500319	−	0.865841i	$-0.666784\pi$
$157$	−12.5380	−1.00064	−0.500319	+	0.865841i	$0.666784\pi$
$158$	9.40559	0.748269
$159$	12.7276	1.00936
$160$	0.118794	0.00939150
$161$	−14.9684	−1.17968
$162$	0.490332	0.0385241
$163$	10.7906	0.845185	0.422593	−	0.906320i	$-0.361120\pi$
$163$	10.7906	0.845185	0.422593	+	0.906320i	$0.361120\pi$
$164$	6.08967	0.475523
$165$	−0.652786	−0.0508193
$166$	−1.93571	−0.150241
$167$	3.91981	0.303324	0.151662	−	0.988432i	$-0.451537\pi$
$167$	3.91981	0.303324	0.151662	+	0.988432i	$0.451537\pi$
$168$	−2.21118	−0.170597
$169$	−12.0909	−0.930069
$170$	−0.167250	−0.0128275
$171$	1.92642	0.147317
$172$	11.1940	0.853537
$173$	−11.5395	−0.877331	−0.438666	−	0.898650i	$-0.644549\pi$
$173$	−11.5395	−0.877331	−0.438666	+	0.898650i	$0.644549\pi$
$174$	3.34371	0.253486
$175$	−10.6402	−0.804323
$176$	5.30344	0.399762
$177$	6.84383	0.514413
$178$	−16.4497	−1.23296
$179$	23.6668	1.76894	0.884469	−	0.466598i	$-0.154521\pi$
$179$	23.6668	1.76894	0.884469	+	0.466598i	$0.154521\pi$
$180$	−0.228847	−0.0170572
$181$	10.4171	0.774295	0.387147	−	0.922018i	$-0.373460\pi$
$181$	10.4171	0.774295	0.387147	+	0.922018i	$0.373460\pi$
$182$	2.03476	0.150826
$183$	−9.31988	−0.688945
$184$	−7.01405	−0.517083
$185$	1.10216	0.0810323
$186$	−6.07852	−0.445699
$187$	−7.46672	−0.546021
$188$	5.03802	0.367435
$189$	10.8932	0.792365
$190$	−0.118794	−0.00861823
$191$	13.9644	1.01043	0.505214	−	0.862994i	$-0.331414\pi$
$191$	13.9644	1.01043	0.505214	+	0.862994i	$0.331414\pi$
$192$	−1.03614	−0.0747769
$193$	−9.29956	−0.669397	−0.334699	−	0.942325i	$-0.608635\pi$
$193$	−9.29956	−0.669397	−0.334699	+	0.942325i	$0.608635\pi$
$194$	−5.85181	−0.420135
$195$	−0.117359	−0.00840428
$196$	−2.44578	−0.174698
$197$	−24.1737	−1.72231	−0.861154	−	0.508344i	$-0.830258\pi$
$197$	−24.1737	−1.72231	−0.861154	+	0.508344i	$0.830258\pi$
$198$	−10.2166	−0.726065
$199$	11.3541	0.804872	0.402436	−	0.915448i	$-0.368164\pi$
$199$	11.3541	0.804872	0.402436	+	0.915448i	$0.368164\pi$
$200$	−4.98589	−0.352556
$201$	−5.69099	−0.401411
$202$	−9.55441	−0.672246
$203$	−6.88680	−0.483359
$204$	1.45878	0.102135
$205$	0.723417	0.0505256
$206$	2.27475	0.158489
$207$	13.5120	0.939148
$208$	0.953466	0.0661110
$209$	−5.30344	−0.366847
$210$	−0.262676	−0.0181263
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−12.2837	−0.843647
$213$	−14.2654	−0.977447
$214$	−6.34312	−0.433606
$215$	1.32978	0.0906906
$216$	5.10445	0.347314
$217$	12.5195	0.849880
$218$	−1.82964	−0.123919
$219$	−13.5114	−0.913018
$220$	0.630018	0.0424758
$221$	−1.34238	−0.0902986
$222$	−9.61318	−0.645195
$223$	−3.96485	−0.265506	−0.132753	−	0.991149i	$-0.542382\pi$
$223$	−3.96485	−0.265506	−0.132753	+	0.991149i	$0.542382\pi$
$224$	2.13406	0.142588
$225$	9.60490	0.640327
$226$	−1.20232	−0.0799774
$227$	−0.200978	−0.0133394	−0.00666969	−	0.999978i	$-0.502123\pi$
$227$	−0.200978	−0.0133394	−0.00666969	+	0.999978i	$0.502123\pi$
$228$	1.03614	0.0686200
$229$	18.2921	1.20877	0.604387	−	0.796691i	$-0.293418\pi$
$229$	18.2921	1.20877	0.604387	+	0.796691i	$0.293418\pi$
$230$	−0.833228	−0.0549414
$231$	−11.7269	−0.771573
$232$	−3.22709	−0.211869
$233$	2.10683	0.138023	0.0690115	−	0.997616i	$-0.478015\pi$
$233$	2.10683	0.138023	0.0690115	+	0.997616i	$0.478015\pi$
$234$	−1.83677	−0.120074
$235$	0.598487	0.0390410
$236$	−6.60513	−0.429957
$237$	−9.74549	−0.633038
$238$	−3.00455	−0.194756
$239$	−14.8788	−0.962430	−0.481215	−	0.876603i	$-0.659804\pi$
$239$	−14.8788	−0.962430	−0.481215	+	0.876603i	$0.659804\pi$
$240$	−0.123087	−0.00794524
$241$	−23.1676	−1.49236	−0.746179	−	0.665745i	$-0.768114\pi$
$241$	−23.1676	−1.49236	−0.746179	+	0.665745i	$0.768114\pi$
$242$	17.1265	1.10093
$243$	−15.8214	−1.01494
$244$	8.99482	0.575834
$245$	−0.290544	−0.0185622
$246$	−6.30974	−0.402294
$247$	−0.953466	−0.0606676
$248$	5.86651	0.372524
$249$	2.00567	0.127104
$250$	−1.18626	−0.0750260
$251$	9.62081	0.607260	0.303630	−	0.952790i	$-0.401801\pi$
$251$	9.62081	0.607260	0.303630	+	0.952790i	$0.401801\pi$
$252$	−4.11109	−0.258975
$253$	−37.1986	−2.33866
$254$	−0.441724	−0.0277162
$255$	0.173294	0.0108521
$256$	1.00000	0.0625000
$257$	25.3603	1.58193	0.790965	−	0.611862i	$-0.209579\pi$
$257$	25.3603	1.58193	0.790965	+	0.611862i	$0.209579\pi$
$258$	−11.5986	−0.722095
$259$	19.7996	1.23029
$260$	0.113266	0.00702447
$261$	6.21672	0.384805
$262$	−2.39368	−0.147882
$263$	3.19578	0.197060	0.0985300	−	0.995134i	$-0.468586\pi$
$263$	3.19578	0.197060	0.0985300	+	0.995134i	$0.468586\pi$
$264$	−5.49510	−0.338200
$265$	−1.45923	−0.0896398
$266$	−2.13406	−0.130848
$267$	17.0442	1.04309
$268$	5.49250	0.335508
$269$	14.4034	0.878192	0.439096	−	0.898440i	$-0.355299\pi$
$269$	14.4034	0.878192	0.439096	+	0.898440i	$0.355299\pi$
$270$	0.606379	0.0369030
$271$	18.6847	1.13501	0.567507	−	0.823369i	$-0.307908\pi$
$271$	18.6847	1.13501	0.567507	+	0.823369i	$0.307908\pi$
$272$	−1.40790	−0.0853665
$273$	−2.10829	−0.127599
$274$	19.6296	1.18587
$275$	−26.4424	−1.59454
$276$	7.26753	0.437454
$277$	25.3666	1.52413	0.762064	−	0.647501i	$-0.224186\pi$
$277$	25.3666	1.52413	0.762064	+	0.647501i	$0.224186\pi$
$278$	2.21189	0.132660
$279$	−11.3014	−0.676594
$280$	0.253514	0.0151504
$281$	13.8266	0.824824	0.412412	−	0.910997i	$-0.364686\pi$
$281$	13.8266	0.824824	0.412412	+	0.910997i	$0.364686\pi$
$282$	−5.22009	−0.310852
$283$	9.96315	0.592248	0.296124	−	0.955150i	$-0.404306\pi$
$283$	9.96315	0.592248	0.296124	+	0.955150i	$0.404306\pi$
$284$	13.7678	0.816970
$285$	0.123087	0.00729105
$286$	5.05665	0.299006
$287$	12.9957	0.767114
$288$	−1.92642	−0.113515
$289$	−15.0178	−0.883401
$290$	−0.383359	−0.0225116
$291$	6.06328	0.355436
$292$	13.0402	0.763119
$293$	17.2137	1.00563	0.502817	−	0.864393i	$-0.332297\pi$
$293$	17.2137	1.00563	0.502817	+	0.864393i	$0.332297\pi$
$294$	2.53417	0.147796
$295$	−0.784650	−0.0456841
$296$	9.27789	0.539267
$297$	27.0712	1.57083
$298$	−2.85546	−0.165412
$299$	−6.68766	−0.386757
$300$	5.16607	0.298263
$301$	23.8888	1.37693
$302$	2.63738	0.151764
$303$	9.89969	0.568722
$304$	−1.00000	−0.0573539
$305$	1.06853	0.0611839
$306$	2.71220	0.155046
$307$	25.4629	1.45324	0.726622	−	0.687038i	$-0.241089\pi$
$307$	25.4629	1.45324	0.726622	+	0.687038i	$0.241089\pi$
$308$	11.3179	0.644896
$309$	−2.35695	−0.134082
$310$	0.696907	0.0395817
$311$	20.4253	1.15821	0.579107	−	0.815252i	$-0.303401\pi$
$311$	20.4253	1.15821	0.579107	+	0.815252i	$0.303401\pi$
$312$	−0.987923	−0.0559301
$313$	4.53190	0.256158	0.128079	−	0.991764i	$-0.459119\pi$
$313$	4.53190	0.256158	0.128079	+	0.991764i	$0.459119\pi$
$314$	−12.5380	−0.707558
$315$	−0.488374	−0.0275167
$316$	9.40559	0.529106
$317$	11.5322	0.647714	0.323857	−	0.946106i	$-0.395020\pi$
$317$	11.5322	0.647714	0.323857	+	0.946106i	$0.395020\pi$
$318$	12.7276	0.713729
$319$	−17.1147	−0.958238
$320$	0.118794	0.00664079
$321$	6.57235	0.366833
$322$	−14.9684	−0.834157
$323$	1.40790	0.0783377
$324$	0.490332	0.0272407
$325$	−4.75387	−0.263697
$326$	10.7906	0.597636
$327$	1.89576	0.104836
$328$	6.08967	0.336246
$329$	10.7515	0.592747
$330$	−0.652786	−0.0359347
$331$	−19.4723	−1.07029	−0.535146	−	0.844759i	$-0.679743\pi$
$331$	−19.4723	−1.07029	−0.535146	+	0.844759i	$0.679743\pi$
$332$	−1.93571	−0.106236
$333$	−17.8731	−0.979439
$334$	3.91981	0.214482
$335$	0.652476	0.0356486
$336$	−2.21118	−0.120630
$337$	26.9628	1.46876	0.734379	−	0.678740i	$-0.237474\pi$
$337$	26.9628	1.46876	0.734379	+	0.678740i	$0.237474\pi$
$338$	−12.0909	−0.657658
$339$	1.24577	0.0676612
$340$	−0.167250	−0.00907042
$341$	31.1127	1.68485
$342$	1.92642	0.104169
$343$	−20.1579	−1.08842
$344$	11.1940	0.603542
$345$	0.863339	0.0464806
$346$	−11.5395	−0.620367
$347$	−2.47186	−0.132696	−0.0663482	−	0.997797i	$-0.521135\pi$
$347$	−2.47186	−0.132696	−0.0663482	+	0.997797i	$0.521135\pi$
$348$	3.34371	0.179242
$349$	4.59571	0.246003	0.123001	−	0.992407i	$-0.460748\pi$
$349$	4.59571	0.246003	0.123001	+	0.992407i	$0.460748\pi$
$350$	−10.6402	−0.568742
$351$	4.86692	0.259777
$352$	5.30344	0.282675
$353$	−0.751216	−0.0399832	−0.0199916	−	0.999800i	$-0.506364\pi$
$353$	−0.751216	−0.0399832	−0.0199916	+	0.999800i	$0.506364\pi$
$354$	6.84383	0.363745
$355$	1.63554	0.0868052
$356$	−16.4497	−0.871833
$357$	3.11313	0.164764
$358$	23.6668	1.25083
$359$	32.4002	1.71002	0.855008	−	0.518614i	$-0.173552\pi$
$359$	32.4002	1.71002	0.855008	+	0.518614i	$0.173552\pi$
$360$	−0.228847	−0.0120613
$361$	1.00000	0.0526316
$362$	10.4171	0.547509
$363$	−17.7454	−0.931394
$364$	2.03476	0.106650
$365$	1.54910	0.0810834
$366$	−9.31988	−0.487158
$367$	33.2882	1.73763	0.868814	−	0.495138i	$-0.164882\pi$
$367$	33.2882	1.73763	0.868814	+	0.495138i	$0.164882\pi$
$368$	−7.01405	−0.365633
$369$	−11.7312	−0.610704
$370$	1.10216	0.0572985
$371$	−26.2142	−1.36097
$372$	−6.07852	−0.315157
$373$	12.4366	0.643942	0.321971	−	0.946749i	$-0.395655\pi$
$373$	12.4366	0.643942	0.321971	+	0.946749i	$0.395655\pi$
$374$	−7.46672	−0.386095
$375$	1.22913	0.0634722
$376$	5.03802	0.259816
$377$	−3.07692	−0.158469
$378$	10.8932	0.560287
$379$	9.39836	0.482762	0.241381	−	0.970430i	$-0.422400\pi$
$379$	9.39836	0.482762	0.241381	+	0.970430i	$0.422400\pi$
$380$	−0.118794	−0.00609401
$381$	0.457687	0.0234480
$382$	13.9644	0.714480
$383$	−14.2944	−0.730407	−0.365204	−	0.930928i	$-0.619001\pi$
$383$	−14.2944	−0.730407	−0.365204	+	0.930928i	$0.619001\pi$
$384$	−1.03614	−0.0528752
$385$	1.34450	0.0685219
$386$	−9.29956	−0.473335
$387$	−21.5644	−1.09618
$388$	−5.85181	−0.297080
$389$	36.3439	1.84271	0.921355	−	0.388723i	$-0.127084\pi$
$389$	36.3439	1.84271	0.921355	+	0.388723i	$0.127084\pi$
$390$	−0.117359	−0.00594272
$391$	9.87508	0.499404
$392$	−2.44578	−0.123530
$393$	2.48019	0.125109
$394$	−24.1737	−1.21786
$395$	1.11733	0.0562189
$396$	−10.2166	−0.513406
$397$	−27.1138	−1.36080	−0.680401	−	0.732840i	$-0.738195\pi$
$397$	−27.1138	−1.36080	−0.680401	+	0.732840i	$0.738195\pi$
$398$	11.3541	0.569130
$399$	2.21118	0.110698
$400$	−4.98589	−0.249294
$401$	20.5133	1.02439	0.512193	−	0.858870i	$-0.328833\pi$
$401$	20.5133	1.02439	0.512193	+	0.858870i	$0.328833\pi$
$402$	−5.69099	−0.283841
$403$	5.59352	0.278633
$404$	−9.55441	−0.475350
$405$	0.0582486	0.00289439
$406$	−6.88680	−0.341786
$407$	49.2048	2.43899
$408$	1.45878	0.0722204
$409$	3.77530	0.186677	0.0933383	−	0.995634i	$-0.470246\pi$
$409$	3.77530	0.186677	0.0933383	+	0.995634i	$0.470246\pi$
$410$	0.723417	0.0357270
$411$	−20.3390	−1.00325
$412$	2.27475	0.112069
$413$	−14.0957	−0.693606
$414$	13.5120	0.664078
$415$	−0.229951	−0.0112879
$416$	0.953466	0.0467475
$417$	−2.29182	−0.112231
$418$	−5.30344	−0.259400
$419$	−24.8611	−1.21455	−0.607273	−	0.794494i	$-0.707736\pi$
$419$	−24.8611	−1.21455	−0.607273	+	0.794494i	$0.707736\pi$
$420$	−0.262676	−0.0128173
$421$	−14.2065	−0.692380	−0.346190	−	0.938164i	$-0.612525\pi$
$421$	−14.2065	−0.692380	−0.346190	+	0.938164i	$0.612525\pi$
$422$	−1.00000	−0.0486792
$423$	−9.70533	−0.471889
$424$	−12.2837	−0.596549
$425$	7.01963	0.340502
$426$	−14.2654	−0.691159
$427$	19.1955	0.928936
$428$	−6.34312	−0.306606
$429$	−5.23939	−0.252960
$430$	1.32978	0.0641279
$431$	−31.1315	−1.49955	−0.749776	−	0.661692i	$-0.769839\pi$
$431$	−31.1315	−1.49955	−0.749776	+	0.661692i	$0.769839\pi$
$432$	5.10445	0.245588
$433$	−14.0770	−0.676500	−0.338250	−	0.941056i	$-0.609835\pi$
$433$	−14.0770	−0.676500	−0.338250	+	0.941056i	$0.609835\pi$
$434$	12.5195	0.600956
$435$	0.397213	0.0190449
$436$	−1.82964	−0.0876240
$437$	7.01405	0.335528
$438$	−13.5114	−0.645601
$439$	15.2653	0.728573	0.364287	−	0.931287i	$-0.381313\pi$
$439$	15.2653	0.728573	0.364287	+	0.931287i	$0.381313\pi$
$440$	0.630018	0.0300349
$441$	4.71159	0.224361
$442$	−1.34238	−0.0638507
$443$	6.44080	0.306012	0.153006	−	0.988225i	$-0.451105\pi$
$443$	6.44080	0.306012	0.153006	+	0.988225i	$0.451105\pi$
$444$	−9.61318	−0.456222
$445$	−1.95413	−0.0926346
$446$	−3.96485	−0.187741
$447$	2.95865	0.139939
$448$	2.13406	0.100825
$449$	−33.6440	−1.58776	−0.793880	−	0.608074i	$-0.791942\pi$
$449$	−33.6440	−1.58776	−0.793880	+	0.608074i	$0.791942\pi$
$450$	9.60490	0.452779
$451$	32.2962	1.52077
$452$	−1.20232	−0.0565526
$453$	−2.73269	−0.128393
$454$	−0.200978	−0.00943236
$455$	0.241717	0.0113319
$456$	1.03614	0.0485216
$457$	−23.7652	−1.11169	−0.555844	−	0.831286i	$-0.687605\pi$
$457$	−23.7652	−1.11169	−0.555844	+	0.831286i	$0.687605\pi$
$458$	18.2921	0.854733
$459$	−7.18656	−0.335440
$460$	−0.833228	−0.0388494
$461$	−33.2389	−1.54809	−0.774045	−	0.633130i	$-0.781770\pi$
$461$	−33.2389	−1.54809	−0.774045	+	0.633130i	$0.781770\pi$
$462$	−11.7269	−0.545584
$463$	−4.13838	−0.192327	−0.0961635	−	0.995366i	$-0.530657\pi$
$463$	−4.13838	−0.192327	−0.0961635	+	0.995366i	$0.530657\pi$
$464$	−3.22709	−0.149814
$465$	−0.722093	−0.0334862
$466$	2.10683	0.0975970
$467$	28.7669	1.33117	0.665586	−	0.746321i	$-0.268182\pi$
$467$	28.7669	1.33117	0.665586	+	0.746321i	$0.268182\pi$
$468$	−1.83677	−0.0849048
$469$	11.7213	0.541241
$470$	0.598487	0.0276062
$471$	12.9911	0.598597
$472$	−6.60513	−0.304026
$473$	59.3669	2.72969
$474$	−9.74549	−0.447625
$475$	4.98589	0.228768
$476$	−3.00455	−0.137713
$477$	23.6635	1.08348
$478$	−14.8788	−0.680541
$479$	−9.34694	−0.427073	−0.213536	−	0.976935i	$-0.568498\pi$
$479$	−9.34694	−0.427073	−0.213536	+	0.976935i	$0.568498\pi$
$480$	−0.123087	−0.00561813
$481$	8.84615	0.403350
$482$	−23.1676	−1.05526
$483$	15.5094	0.705700
$484$	17.1265	0.778478
$485$	−0.695160	−0.0315656
$486$	−15.8214	−0.717673
$487$	3.81019	0.172656	0.0863280	−	0.996267i	$-0.472487\pi$
$487$	3.81019	0.172656	0.0863280	+	0.996267i	$0.472487\pi$
$488$	8.99482	0.407176
$489$	−11.1806	−0.505602
$490$	−0.290544	−0.0131254
$491$	3.90927	0.176423	0.0882113	−	0.996102i	$-0.471885\pi$
$491$	3.90927	0.176423	0.0882113	+	0.996102i	$0.471885\pi$
$492$	−6.30974	−0.284465
$493$	4.54342	0.204625
$494$	−0.953466	−0.0428985
$495$	−1.21368	−0.0545507
$496$	5.86651	0.263414
$497$	29.3814	1.31793
$498$	2.00567	0.0898761
$499$	−25.8060	−1.15524	−0.577618	−	0.816307i	$-0.696018\pi$
$499$	−25.8060	−1.15524	−0.577618	+	0.816307i	$0.696018\pi$
$500$	−1.18626	−0.0530514
$501$	−4.06147	−0.181453
$502$	9.62081	0.429398
$503$	−4.32665	−0.192916	−0.0964580	−	0.995337i	$-0.530751\pi$
$503$	−4.32665	−0.192916	−0.0964580	+	0.995337i	$0.530751\pi$
$504$	−4.11109	−0.183123
$505$	−1.13501	−0.0505072
$506$	−37.1986	−1.65368
$507$	12.5279	0.556381
$508$	−0.441724	−0.0195983
$509$	−21.4576	−0.951093	−0.475547	−	0.879690i	$-0.657750\pi$
$509$	−21.4576	−0.951093	−0.475547	+	0.879690i	$0.657750\pi$
$510$	0.173294	0.00767361
$511$	27.8286	1.23106
$512$	1.00000	0.0441942
$513$	−5.10445	−0.225367
$514$	25.3603	1.11859
$515$	0.270226	0.0119076
$516$	−11.5986	−0.510599
$517$	26.7189	1.17509
$518$	19.7996	0.869945
$519$	11.9565	0.524832
$520$	0.113266	0.00496705
$521$	25.3942	1.11254	0.556269	−	0.831002i	$-0.312232\pi$
$521$	25.3942	1.11254	0.556269	+	0.831002i	$0.312232\pi$
$522$	6.21672	0.272098
$523$	−21.0553	−0.920684	−0.460342	−	0.887742i	$-0.652273\pi$
$523$	−21.0553	−0.920684	−0.460342	+	0.887742i	$0.652273\pi$
$524$	−2.39368	−0.104568
$525$	11.0247	0.481158
$526$	3.19578	0.139342
$527$	−8.25947	−0.359788
$528$	−5.49510	−0.239144
$529$	26.1969	1.13900
$530$	−1.45923	−0.0633849
$531$	12.7242	0.552184
$532$	−2.13406	−0.0925233
$533$	5.80629	0.251498
$534$	17.0442	0.737574
$535$	−0.753525	−0.0325777
$536$	5.49250	0.237240
$537$	−24.5221	−1.05821
$538$	14.4034	0.620975
$539$	−12.9711	−0.558703
$540$	0.606379	0.0260944
$541$	−26.6048	−1.14383	−0.571914	−	0.820313i	$-0.693799\pi$
$541$	−26.6048	−1.14383	−0.571914	+	0.820313i	$0.693799\pi$
$542$	18.6847	0.802575
$543$	−10.7935	−0.463195
$544$	−1.40790	−0.0603632
$545$	−0.217351	−0.00931028
$546$	−2.10829	−0.0902264
$547$	−29.3789	−1.25615	−0.628075	−	0.778152i	$-0.716157\pi$
$547$	−29.3789	−1.25615	−0.628075	+	0.778152i	$0.716157\pi$
$548$	19.6296	0.838536
$549$	−17.3278	−0.739531
$550$	−26.4424	−1.12751
$551$	3.22709	0.137479
$552$	7.26753	0.309327
$553$	20.0721	0.853553
$554$	25.3666	1.07772
$555$	−1.14199	−0.0484748
$556$	2.21189	0.0938048
$557$	−20.7385	−0.878719	−0.439359	−	0.898311i	$-0.644794\pi$
$557$	−20.7385	−0.878719	−0.439359	+	0.898311i	$0.644794\pi$
$558$	−11.3014	−0.478424
$559$	10.6731	0.451425
$560$	0.253514	0.0107129
$561$	7.73656	0.326638
$562$	13.8266	0.583239
$563$	35.4515	1.49410	0.747051	−	0.664767i	$-0.231469\pi$
$563$	35.4515	1.49410	0.747051	+	0.664767i	$0.231469\pi$
$564$	−5.22009	−0.219805
$565$	−0.142829	−0.00600886
$566$	9.96315	0.418782
$567$	1.04640	0.0439446
$568$	13.7678	0.577685
$569$	−41.3306	−1.73267	−0.866335	−	0.499463i	$-0.833531\pi$
$569$	−41.3306	−1.73267	−0.866335	+	0.499463i	$0.833531\pi$
$570$	0.123087	0.00515555
$571$	−44.1532	−1.84775	−0.923876	−	0.382691i	$-0.874997\pi$
$571$	−44.1532	−1.84775	−0.923876	+	0.382691i	$0.874997\pi$
$572$	5.05665	0.211429
$573$	−14.4690	−0.604453
$574$	12.9957	0.542431
$575$	34.9713	1.45840
$576$	−1.92642	−0.0802674
$577$	14.7346	0.613410	0.306705	−	0.951805i	$-0.400773\pi$
$577$	14.7346	0.613410	0.306705	+	0.951805i	$0.400773\pi$
$578$	−15.0178	−0.624659
$579$	9.63564	0.400443
$580$	−0.383359	−0.0159181
$581$	−4.13093	−0.171380
$582$	6.06328	0.251331
$583$	−65.1459	−2.69807
$584$	13.0402	0.539607
$585$	−0.218198	−0.00902137
$586$	17.2137	0.711091
$587$	−42.7940	−1.76630	−0.883148	−	0.469095i	$-0.844580\pi$
$587$	−42.7940	−1.76630	−0.883148	+	0.469095i	$0.844580\pi$
$588$	2.53417	0.104507
$589$	−5.86651	−0.241726
$590$	−0.784650	−0.0323035
$591$	25.0474	1.03031
$592$	9.27789	0.381319
$593$	27.9183	1.14647	0.573234	−	0.819392i	$-0.305689\pi$
$593$	27.9183	1.14647	0.573234	+	0.819392i	$0.305689\pi$
$594$	27.0712	1.11074
$595$	−0.356922	−0.0146324
$596$	−2.85546	−0.116964
$597$	−11.7644	−0.481486
$598$	−6.68766	−0.273479
$599$	−14.4316	−0.589658	−0.294829	−	0.955550i	$-0.595263\pi$
$599$	−14.4316	−0.589658	−0.294829	+	0.955550i	$0.595263\pi$
$600$	5.16607	0.210904
$601$	−3.58400	−0.146195	−0.0730973	−	0.997325i	$-0.523288\pi$
$601$	−3.58400	−0.146195	−0.0730973	+	0.997325i	$0.523288\pi$
$602$	23.8888	0.973633
$603$	−10.5808	−0.430885
$604$	2.63738	0.107313
$605$	2.03453	0.0827154
$606$	9.89969	0.402147
$607$	−33.7077	−1.36815	−0.684077	−	0.729410i	$-0.739795\pi$
$607$	−33.7077	−1.36815	−0.684077	+	0.729410i	$0.739795\pi$
$608$	−1.00000	−0.0405554
$609$	7.13568	0.289153
$610$	1.06853	0.0432636
$611$	4.80358	0.194332
$612$	2.71220	0.109634
$613$	−12.5034	−0.505008	−0.252504	−	0.967596i	$-0.581254\pi$
$613$	−12.5034	−0.505008	−0.252504	+	0.967596i	$0.581254\pi$
$614$	25.4629	1.02760
$615$	−0.749560	−0.0302252
$616$	11.3179	0.456010
$617$	8.04213	0.323764	0.161882	−	0.986810i	$-0.448244\pi$
$617$	8.04213	0.323764	0.161882	+	0.986810i	$0.448244\pi$
$618$	−2.35695	−0.0948105
$619$	−30.5719	−1.22879	−0.614393	−	0.789000i	$-0.710599\pi$
$619$	−30.5719	−1.22879	−0.614393	+	0.789000i	$0.710599\pi$
$620$	0.696907	0.0279885
$621$	−35.8029	−1.43672
$622$	20.4253	0.818981
$623$	−35.1047	−1.40644
$624$	−0.987923	−0.0395486
$625$	24.7885	0.991541
$626$	4.53190	0.181131
$627$	5.49510	0.219453
$628$	−12.5380	−0.500319
$629$	−13.0623	−0.520830
$630$	−0.488374	−0.0194573
$631$	17.9056	0.712811	0.356405	−	0.934331i	$-0.384002\pi$
$631$	17.9056	0.712811	0.356405	+	0.934331i	$0.384002\pi$
$632$	9.40559	0.374134
$633$	1.03614	0.0411828
$634$	11.5322	0.458003
$635$	−0.0524742	−0.00208237
$636$	12.7276	0.504682
$637$	−2.33197	−0.0923959
$638$	−17.1147	−0.677577
$639$	−26.5226	−1.04922
$640$	0.118794	0.00469575
$641$	19.3598	0.764667	0.382334	−	0.924024i	$-0.375121\pi$
$641$	19.3598	0.764667	0.382334	+	0.924024i	$0.375121\pi$
$642$	6.57235	0.259390
$643$	−26.3700	−1.03993	−0.519965	−	0.854187i	$-0.674055\pi$
$643$	−26.3700	−1.03993	−0.519965	+	0.854187i	$0.674055\pi$
$644$	−14.9684	−0.589838
$645$	−1.37784	−0.0542525
$646$	1.40790	0.0553931
$647$	−39.8331	−1.56600	−0.783001	−	0.622021i	$-0.786312\pi$
$647$	−39.8331	−1.56600	−0.783001	+	0.622021i	$0.786312\pi$
$648$	0.490332	0.0192621
$649$	−35.0299	−1.37504
$650$	−4.75387	−0.186462
$651$	−12.9719	−0.508411
$652$	10.7906	0.422593
$653$	−0.632296	−0.0247437	−0.0123718	−	0.999923i	$-0.503938\pi$
$653$	−0.632296	−0.0247437	−0.0123718	+	0.999923i	$0.503938\pi$
$654$	1.89576	0.0741302
$655$	−0.284355	−0.0111107
$656$	6.08967	0.237762
$657$	−25.1208	−0.980057
$658$	10.7515	0.419135
$659$	5.01220	0.195248	0.0976239	−	0.995223i	$-0.468876\pi$
$659$	5.01220	0.195248	0.0976239	+	0.995223i	$0.468876\pi$
$660$	−0.652786	−0.0254097
$661$	−3.04793	−0.118551	−0.0592753	−	0.998242i	$-0.518879\pi$
$661$	−3.04793	−0.118551	−0.0592753	+	0.998242i	$0.518879\pi$
$662$	−19.4723	−0.756811
$663$	1.39090	0.0540179
$664$	−1.93571	−0.0751203
$665$	−0.253514	−0.00983085
$666$	−17.8731	−0.692568
$667$	22.6350	0.876429
$668$	3.91981	0.151662
$669$	4.10814	0.158830
$670$	0.652476	0.0252074
$671$	47.7035	1.84157
$672$	−2.21118	−0.0852983
$673$	−0.735886	−0.0283663	−0.0141832	−	0.999899i	$-0.504515\pi$
$673$	−0.735886	−0.0283663	−0.0141832	+	0.999899i	$0.504515\pi$
$674$	26.9628	1.03857
$675$	−25.4502	−0.979579
$676$	−12.0909	−0.465035
$677$	−21.9886	−0.845090	−0.422545	−	0.906342i	$-0.638863\pi$
$677$	−21.9886	−0.845090	−0.422545	+	0.906342i	$0.638863\pi$
$678$	1.24577	0.0478437
$679$	−12.4881	−0.479250
$680$	−0.167250	−0.00641375
$681$	0.208241	0.00797981
$682$	31.1127	1.19137
$683$	42.4553	1.62451	0.812254	−	0.583304i	$-0.198240\pi$
$683$	42.4553	1.62451	0.812254	+	0.583304i	$0.198240\pi$
$684$	1.92642	0.0736584
$685$	2.33188	0.0890966
$686$	−20.1579	−0.769631
$687$	−18.9531	−0.723107
$688$	11.1940	0.426768
$689$	−11.7121	−0.446195
$690$	0.863339	0.0328668
$691$	18.9771	0.721921	0.360961	−	0.932581i	$-0.382449\pi$
$691$	18.9771	0.721921	0.360961	+	0.932581i	$0.382449\pi$
$692$	−11.5395	−0.438666
$693$	−21.8030	−0.828226
$694$	−2.47186	−0.0938305
$695$	0.262759	0.00996701
$696$	3.34371	0.126743
$697$	−8.57364	−0.324750
$698$	4.59571	0.173950
$699$	−2.18297	−0.0825674
$700$	−10.6402	−0.402162
$701$	−19.1532	−0.723405	−0.361703	−	0.932294i	$-0.617804\pi$
$701$	−19.1532	−0.723405	−0.361703	+	0.932294i	$0.617804\pi$
$702$	4.86692	0.183690
$703$	−9.27789	−0.349922
$704$	5.30344	0.199881
$705$	−0.620116	−0.0233549
$706$	−0.751216	−0.0282724
$707$	−20.3897	−0.766834
$708$	6.84383	0.257207
$709$	−30.8487	−1.15855	−0.579274	−	0.815133i	$-0.696664\pi$
$709$	−30.8487	−1.15855	−0.579274	+	0.815133i	$0.696664\pi$
$710$	1.63554	0.0613806
$711$	−18.1191	−0.679519
$712$	−16.4497	−0.616479
$713$	−41.1480	−1.54101
$714$	3.11313	0.116506
$715$	0.600700	0.0224649
$716$	23.6668	0.884469
$717$	15.4165	0.575740
$718$	32.4002	1.20916
$719$	−34.7621	−1.29641	−0.648203	−	0.761467i	$-0.724479\pi$
$719$	−34.7621	−1.29641	−0.648203	+	0.761467i	$0.724479\pi$
$720$	−0.228847	−0.00852862
$721$	4.85445	0.180789
$722$	1.00000	0.0372161
$723$	24.0049	0.892751
$724$	10.4171	0.387147
$725$	16.0899	0.597564
$726$	−17.7454	−0.658595
$727$	−6.96965	−0.258490	−0.129245	−	0.991613i	$-0.541255\pi$
$727$	−6.96965	−0.258490	−0.129245	+	0.991613i	$0.541255\pi$
$728$	2.03476	0.0754130
$729$	14.9222	0.552673
$730$	1.54910	0.0573346
$731$	−15.7601	−0.582908
$732$	−9.31988	−0.344473
$733$	7.43849	0.274747	0.137374	−	0.990519i	$-0.456134\pi$
$733$	7.43849	0.274747	0.137374	+	0.990519i	$0.456134\pi$
$734$	33.2882	1.22869
$735$	0.301044	0.0111042
$736$	−7.01405	−0.258541
$737$	29.1292	1.07299
$738$	−11.7312	−0.431833
$739$	48.3900	1.78006	0.890028	−	0.455907i	$-0.150685\pi$
$739$	48.3900	1.78006	0.890028	+	0.455907i	$0.150685\pi$
$740$	1.10216	0.0405162
$741$	0.987923	0.0362922
$742$	−26.2142	−0.962352
$743$	10.7258	0.393491	0.196746	−	0.980455i	$-0.436963\pi$
$743$	10.7258	0.393491	0.196746	+	0.980455i	$0.436963\pi$
$744$	−6.07852	−0.222849
$745$	−0.339211	−0.0124277
$746$	12.4366	0.455336
$747$	3.72899	0.136437
$748$	−7.46672	−0.273010
$749$	−13.5366	−0.494617
$750$	1.22913	0.0448816
$751$	−52.5013	−1.91580	−0.957900	−	0.287102i	$-0.907308\pi$
$751$	−52.5013	−1.91580	−0.957900	+	0.287102i	$0.907308\pi$
$752$	5.03802	0.183718
$753$	−9.96850	−0.363272
$754$	−3.07692	−0.112055
$755$	0.313305	0.0114023
$756$	10.8932	0.396182
$757$	−35.8842	−1.30423	−0.652116	−	0.758119i	$-0.726118\pi$
$757$	−35.8842	−1.30423	−0.652116	+	0.758119i	$0.726118\pi$
$758$	9.39836	0.341364
$759$	38.5429	1.39902
$760$	−0.118794	−0.00430911
$761$	35.6762	1.29326	0.646631	−	0.762803i	$-0.276178\pi$
$761$	35.6762	1.29326	0.646631	+	0.762803i	$0.276178\pi$
$762$	0.457687	0.0165803
$763$	−3.90457	−0.141355
$764$	13.9644	0.505214
$765$	0.322194	0.0116489
$766$	−14.2944	−0.516476
$767$	−6.29776	−0.227399
$768$	−1.03614	−0.0373884
$769$	39.4352	1.42207	0.711034	−	0.703157i	$-0.248227\pi$
$769$	39.4352	1.42207	0.711034	+	0.703157i	$0.248227\pi$
$770$	1.34450	0.0484523
$771$	−26.2767	−0.946334
$772$	−9.29956	−0.334699
$773$	24.5772	0.883980	0.441990	−	0.897020i	$-0.354273\pi$
$773$	24.5772	0.883980	0.441990	+	0.897020i	$0.354273\pi$
$774$	−21.5644	−0.775115
$775$	−29.2498	−1.05068
$776$	−5.85181	−0.210068
$777$	−20.5151	−0.735976
$778$	36.3439	1.30299
$779$	−6.08967	−0.218185
$780$	−0.117359	−0.00420214
$781$	73.0169	2.61275
$782$	9.87508	0.353132
$783$	−16.4725	−0.588679
$784$	−2.44578	−0.0873492
$785$	−1.48944	−0.0531602
$786$	2.48019	0.0884653
$787$	−29.1101	−1.03766	−0.518832	−	0.854877i	$-0.673633\pi$
$787$	−29.1101	−1.03766	−0.518832	+	0.854877i	$0.673633\pi$
$788$	−24.1737	−0.861154
$789$	−3.31127	−0.117884
$790$	1.11733	0.0397528
$791$	−2.56583	−0.0912306
$792$	−10.2166	−0.363033
$793$	8.57625	0.304552
$794$	−27.1138	−0.962233
$795$	1.51196	0.0536239
$796$	11.3541	0.402436
$797$	22.2340	0.787570	0.393785	−	0.919203i	$-0.371165\pi$
$797$	22.2340	0.787570	0.393785	+	0.919203i	$0.371165\pi$
$798$	2.21118	0.0782751
$799$	−7.09303	−0.250933
$800$	−4.98589	−0.176278
$801$	31.6890	1.11968
$802$	20.5133	0.724350
$803$	69.1579	2.44053
$804$	−5.69099	−0.200706
$805$	−1.77816	−0.0626719
$806$	5.59352	0.197023
$807$	−14.9239	−0.525347
$808$	−9.55441	−0.336123
$809$	−29.2975	−1.03004	−0.515022	−	0.857177i	$-0.672216\pi$
$809$	−29.2975	−1.03004	−0.515022	+	0.857177i	$0.672216\pi$
$810$	0.0582486	0.00204665
$811$	47.2019	1.65748	0.828741	−	0.559632i	$-0.189057\pi$
$811$	47.2019	1.65748	0.828741	+	0.559632i	$0.189057\pi$
$812$	−6.88680	−0.241679
$813$	−19.3599	−0.678982
$814$	49.2048	1.72463
$815$	1.28186	0.0449016
$816$	1.45878	0.0510675
$817$	−11.1940	−0.391630
$818$	3.77530	0.132000
$819$	−3.91979	−0.136968
$820$	0.723417	0.0252628
$821$	−0.369387	−0.0128917	−0.00644584	−	0.999979i	$-0.502052\pi$
$821$	−0.369387	−0.0128917	−0.00644584	+	0.999979i	$0.502052\pi$
$822$	−20.3390	−0.709404
$823$	−4.59959	−0.160332	−0.0801658	−	0.996782i	$-0.525545\pi$
$823$	−4.59959	−0.160332	−0.0801658	+	0.996782i	$0.525545\pi$
$824$	2.27475	0.0792445
$825$	27.3980	0.953875
$826$	−14.0957	−0.490454
$827$	−43.8348	−1.52429	−0.762143	−	0.647409i	$-0.775852\pi$
$827$	−43.8348	−1.52429	−0.762143	+	0.647409i	$0.775852\pi$
$828$	13.5120	0.469574
$829$	43.5645	1.51306	0.756528	−	0.653961i	$-0.226894\pi$
$829$	43.5645	1.51306	0.756528	+	0.653961i	$0.226894\pi$
$830$	−0.229951	−0.00798173
$831$	−26.2833	−0.911756
$832$	0.953466	0.0330555
$833$	3.44341	0.119307
$834$	−2.29182	−0.0793592
$835$	0.465650	0.0161145
$836$	−5.30344	−0.183423
$837$	29.9453	1.03506
$838$	−24.8611	−0.858813
$839$	12.8343	0.443088	0.221544	−	0.975150i	$-0.428890\pi$
$839$	12.8343	0.443088	0.221544	+	0.975150i	$0.428890\pi$
$840$	−0.262676	−0.00906317
$841$	−18.5859	−0.640893
$842$	−14.2065	−0.489587
$843$	−14.3262	−0.493422
$844$	−1.00000	−0.0344214
$845$	−1.43633	−0.0494112
$846$	−9.70533	−0.333676
$847$	36.5491	1.25584
$848$	−12.2837	−0.421824
$849$	−10.3232	−0.354291
$850$	7.01963	0.240771
$851$	−65.0756	−2.23076
$852$	−14.2654	−0.488723
$853$	4.62872	0.158484	0.0792421	−	0.996855i	$-0.474750\pi$
$853$	4.62872	0.158484	0.0792421	+	0.996855i	$0.474750\pi$
$854$	19.1955	0.656857
$855$	0.228847	0.00782640
$856$	−6.34312	−0.216803
$857$	−31.3069	−1.06942	−0.534712	−	0.845034i	$-0.679580\pi$
$857$	−31.3069	−1.06942	−0.534712	+	0.845034i	$0.679580\pi$
$858$	−5.23939	−0.178870
$859$	−44.5647	−1.52053	−0.760263	−	0.649615i	$-0.774930\pi$
$859$	−44.5647	−1.52053	−0.760263	+	0.649615i	$0.774930\pi$
$860$	1.32978	0.0453453
$861$	−13.4654	−0.458899
$862$	−31.1315	−1.06034
$863$	35.0485	1.19307	0.596533	−	0.802589i	$-0.296544\pi$
$863$	35.0485	1.19307	0.596533	+	0.802589i	$0.296544\pi$
$864$	5.10445	0.173657
$865$	−1.37082	−0.0466094
$866$	−14.0770	−0.478357
$867$	15.5605	0.528464
$868$	12.5195	0.424940
$869$	49.8820	1.69213
$870$	0.397213	0.0134668
$871$	5.23691	0.177446
$872$	−1.82964	−0.0619595
$873$	11.2730	0.381534
$874$	7.01405	0.237254
$875$	−2.53156	−0.0855824
$876$	−13.5114	−0.456509
$877$	36.4438	1.23062	0.615310	−	0.788285i	$-0.289031\pi$
$877$	36.4438	1.23062	0.615310	+	0.788285i	$0.289031\pi$
$878$	15.2653	0.515179
$879$	−17.8358	−0.601586
$880$	0.630018	0.0212379
$881$	−6.93642	−0.233694	−0.116847	−	0.993150i	$-0.537279\pi$
$881$	−6.93642	−0.233694	−0.116847	+	0.993150i	$0.537279\pi$
$882$	4.71159	0.158647
$883$	41.5904	1.39963	0.699814	−	0.714325i	$-0.253266\pi$
$883$	41.5904	1.39963	0.699814	+	0.714325i	$0.253266\pi$
$884$	−1.34238	−0.0451493
$885$	0.813006	0.0273289
$886$	6.44080	0.216383
$887$	33.7553	1.13339	0.566696	−	0.823927i	$-0.308221\pi$
$887$	33.7553	1.13339	0.566696	+	0.823927i	$0.308221\pi$
$888$	−9.61318	−0.322597
$889$	−0.942666	−0.0316160
$890$	−1.95413	−0.0655026
$891$	2.60045	0.0871183
$892$	−3.96485	−0.132753
$893$	−5.03802	−0.168591
$894$	2.95865	0.0989520
$895$	2.81147	0.0939772
$896$	2.13406	0.0712940
$897$	6.92934	0.231364
$898$	−33.6440	−1.12272
$899$	−18.9318	−0.631409
$900$	9.60490	0.320163
$901$	17.2942	0.576154
$902$	32.2962	1.07535
$903$	−24.7521	−0.823697
$904$	−1.20232	−0.0399887
$905$	1.23749	0.0411354
$906$	−2.73269	−0.0907875
$907$	−14.0894	−0.467832	−0.233916	−	0.972257i	$-0.575154\pi$
$907$	−14.0894	−0.467832	−0.233916	+	0.972257i	$0.575154\pi$
$908$	−0.200978	−0.00666969
$909$	18.4058	0.610481
$910$	0.241717	0.00801284
$911$	−14.5143	−0.480881	−0.240440	−	0.970664i	$-0.577292\pi$
$911$	−14.5143	−0.480881	−0.240440	+	0.970664i	$0.577292\pi$
$912$	1.03614	0.0343100
$913$	−10.2660	−0.339753
$914$	−23.7652	−0.786082
$915$	−1.10715	−0.0366011
$916$	18.2921	0.604387
$917$	−5.10827	−0.168690
$918$	−7.18656	−0.237192
$919$	11.8884	0.392163	0.196081	−	0.980588i	$-0.437178\pi$
$919$	11.8884	0.392163	0.196081	+	0.980588i	$0.437178\pi$
$920$	−0.833228	−0.0274707
$921$	−26.3831	−0.869352
$922$	−33.2389	−1.09467
$923$	13.1271	0.432085
$924$	−11.7269	−0.385786
$925$	−46.2585	−1.52097
$926$	−4.13838	−0.135996
$927$	−4.38211	−0.143927
$928$	−3.22709	−0.105934
$929$	−19.8014	−0.649663	−0.324832	−	0.945772i	$-0.605308\pi$
$929$	−19.8014	−0.649663	−0.324832	+	0.945772i	$0.605308\pi$
$930$	−0.722093	−0.0236783
$931$	2.44578	0.0801572
$932$	2.10683	0.0690115
$933$	−21.1635	−0.692860
$934$	28.7669	0.941281
$935$	−0.887002	−0.0290081
$936$	−1.83677	−0.0600368
$937$	34.2583	1.11917	0.559585	−	0.828773i	$-0.310961\pi$
$937$	34.2583	1.11917	0.559585	+	0.828773i	$0.310961\pi$
$938$	11.7213	0.382715
$939$	−4.69567	−0.153237
$940$	0.598487	0.0195205
$941$	−0.766759	−0.0249956	−0.0124978	−	0.999922i	$-0.503978\pi$
$941$	−0.766759	−0.0249956	−0.0124978	+	0.999922i	$0.503978\pi$
$942$	12.9911	0.423272
$943$	−42.7132	−1.39093
$944$	−6.60513	−0.214979
$945$	1.29405	0.0420954
$946$	59.3669	1.93019
$947$	20.4260	0.663757	0.331878	−	0.943322i	$-0.392318\pi$
$947$	20.4260	0.663757	0.331878	+	0.943322i	$0.392318\pi$
$948$	−9.74549	−0.316519
$949$	12.4334	0.403604
$950$	4.98589	0.161764
$951$	−11.9490	−0.387472
$952$	−3.00455	−0.0973779
$953$	−2.85501	−0.0924829	−0.0462414	−	0.998930i	$-0.514724\pi$
$953$	−2.85501	−0.0924829	−0.0462414	+	0.998930i	$0.514724\pi$
$954$	23.6635	0.766134
$955$	1.65889	0.0536803
$956$	−14.8788	−0.481215
$957$	17.7332	0.573232
$958$	−9.34694	−0.301986
$959$	41.8908	1.35273
$960$	−0.123087	−0.00397262
$961$	3.41600	0.110193
$962$	8.84615	0.285211
$963$	12.2195	0.393767
$964$	−23.1676	−0.746179
$965$	−1.10473	−0.0355626
$966$	15.5094	0.499005
$967$	60.1612	1.93466	0.967328	−	0.253530i	$-0.0815916\pi$
$967$	60.1612	1.93466	0.967328	+	0.253530i	$0.0815916\pi$
$968$	17.1265	0.550467
$969$	−1.45878	−0.0468628
$970$	−0.695160	−0.0223202
$971$	−45.6797	−1.46593	−0.732965	−	0.680266i	$-0.761864\pi$
$971$	−45.6797	−1.46593	−0.732965	+	0.680266i	$0.761864\pi$
$972$	−15.8214	−0.507472
$973$	4.72030	0.151326
$974$	3.81019	0.122086
$975$	4.92567	0.157748
$976$	8.99482	0.287917
$977$	46.3154	1.48176	0.740880	−	0.671638i	$-0.234409\pi$
$977$	46.3154	1.48176	0.740880	+	0.671638i	$0.234409\pi$
$978$	−11.1806	−0.357515
$979$	−87.2402	−2.78821
$980$	−0.290544	−0.00928109
$981$	3.52465	0.112534
$982$	3.90927	0.124750
$983$	−28.6791	−0.914722	−0.457361	−	0.889281i	$-0.651205\pi$
$983$	−28.6791	−0.914722	−0.457361	+	0.889281i	$0.651205\pi$
$984$	−6.30974	−0.201147
$985$	−2.87170	−0.0914999
$986$	4.54342	0.144692
$987$	−11.1400	−0.354590
$988$	−0.953466	−0.0303338
$989$	−78.5155	−2.49665
$990$	−1.21368	−0.0385732
$991$	39.1355	1.24318	0.621590	−	0.783343i	$-0.286487\pi$
$991$	39.1355	1.24318	0.621590	+	0.783343i	$0.286487\pi$
$992$	5.86651	0.186262
$993$	20.1760	0.640265
$994$	29.3814	0.931921
$995$	1.34880	0.0427599
$996$	2.00567	0.0635520
$997$	26.3862	0.835660	0.417830	−	0.908525i	$-0.362791\pi$
$997$	26.3862	0.835660	0.417830	+	0.908525i	$0.362791\pi$
$998$	−25.8060	−0.816875
$999$	47.3585	1.49836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.17	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.17	✓	47	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.03614 q^{3} +1.00000 q^{4} +0.118794 q^{5} -1.03614 q^{6} +2.13406 q^{7} +1.00000 q^{8} -1.92642 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.03614 q^{3} +1.00000 q^{4} +0.118794 q^{5} -1.03614 q^{6} +2.13406 q^{7} +1.00000 q^{8} -1.92642 q^{9} +0.118794 q^{10} +5.30344 q^{11} -1.03614 q^{12} +0.953466 q^{13} +2.13406 q^{14} -0.123087 q^{15} +1.00000 q^{16} -1.40790 q^{17} -1.92642 q^{18} -1.00000 q^{19} +0.118794 q^{20} -2.21118 q^{21} +5.30344 q^{22} -7.01405 q^{23} -1.03614 q^{24} -4.98589 q^{25} +0.953466 q^{26} +5.10445 q^{27} +2.13406 q^{28} -3.22709 q^{29} -0.123087 q^{30} +5.86651 q^{31} +1.00000 q^{32} -5.49510 q^{33} -1.40790 q^{34} +0.253514 q^{35} -1.92642 q^{36} +9.27789 q^{37} -1.00000 q^{38} -0.987923 q^{39} +0.118794 q^{40} +6.08967 q^{41} -2.21118 q^{42} +11.1940 q^{43} +5.30344 q^{44} -0.228847 q^{45} -7.01405 q^{46} +5.03802 q^{47} -1.03614 q^{48} -2.44578 q^{49} -4.98589 q^{50} +1.45878 q^{51} +0.953466 q^{52} -12.2837 q^{53} +5.10445 q^{54} +0.630018 q^{55} +2.13406 q^{56} +1.03614 q^{57} -3.22709 q^{58} -6.60513 q^{59} -0.123087 q^{60} +8.99482 q^{61} +5.86651 q^{62} -4.11109 q^{63} +1.00000 q^{64} +0.113266 q^{65} -5.49510 q^{66} +5.49250 q^{67} -1.40790 q^{68} +7.26753 q^{69} +0.253514 q^{70} +13.7678 q^{71} -1.92642 q^{72} +13.0402 q^{73} +9.27789 q^{74} +5.16607 q^{75} -1.00000 q^{76} +11.3179 q^{77} -0.987923 q^{78} +9.40559 q^{79} +0.118794 q^{80} +0.490332 q^{81} +6.08967 q^{82} -1.93571 q^{83} -2.21118 q^{84} -0.167250 q^{85} +11.1940 q^{86} +3.34371 q^{87} +5.30344 q^{88} -16.4497 q^{89} -0.228847 q^{90} +2.03476 q^{91} -7.01405 q^{92} -6.07852 q^{93} +5.03802 q^{94} -0.118794 q^{95} -1.03614 q^{96} -5.85181 q^{97} -2.44578 q^{98} -10.2166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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